Articles containing proofs | Theorems in projective geometry | Conic sections | Theorems about polygons | Euclidean plane geometry

Pascal's theorem

In projective geometry, Pascal's theorem (also known as the hexagrammum mysticum theorem) states that if six arbitrary points are chosen on a conic (which may be an ellipse, parabola or hyperbola in an appropriate affine plane) and joined by line segments in any order to form a hexagon, then the three pairs of opposite sides of the hexagon (extended if necessary) meet at three points which lie on a straight line, called the Pascal line of the hexagon. It is named after Blaise Pascal. The theorem is also valid in the Euclidean plane, but the statement needs to be adjusted to deal with the special cases when opposite sides are parallel. This theorem is a generalization of Pappus's (hexagon) theorem, which is the special case of a degenerate conic of two lines with three points on each line. (Wikipedia).

Pascal's theorem
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Images in Math - Pascal's Theorem

This video is about Pascal's Theorem.

From playlist Images in Math

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Calculus 5.3 The Fundamental Theorem of Calculus

My notes are available at http://asherbroberts.com/ (so you can write along with me). Calculus: Early Transcendentals 8th Edition by James Stewart

From playlist Calculus

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Calculus - The Fundamental Theorem, Part 1

The Fundamental Theorem of Calculus. First video in a short series on the topic. The theorem is stated and two simple examples are worked.

From playlist Calculus - The Fundamental Theorem of Calculus

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Discrete Math: 02. Rowsums of Pascal's Triangle

The rowsums of Pascal's Triangle are always powers of 2. Here I provide a combinatorial proof of this fact. The proof involves a very useful technique involving sequences of 0's and 1's. I describe the technique using a small example before moving to the general proof. --An introduction

From playlist Discrete Math part-1

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Discrete Math: 03. Combinatorial Proof on Pascal's Triangle

There is a straightforward way to build Pascal's Triangle by defining the value of a term to be the the sum of the adjacent two entries in the row above it. We also know that Pascal's Triangle contains the binomial coefficients nCk. In this video I provide a combinatorial proof to show w

From playlist Discrete Math part-1

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Calculus - The Fundamental Theorem, Part 3

The Fundamental Theorem of Calculus. Specific examples of simple functions, and how the antiderivative of these functions relates to the area under the graph.

From playlist Calculus - The Fundamental Theorem of Calculus

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Pascal's Triangle and Binomial Theorem - The Connection

Exploring the relation between the Pascal's Triangle and the Binomial Theorem - why the binomial coefficients of nth power correspond to the values in the nth row of the triangle. Timestamps : 0:00 Introduction 2:50 nCr 4:44 Identity 7:35 nCr to Pascal's Triangle 12:40 Binomial to Pascal

From playlist Summer of Math Exposition Youtube Videos

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Calculus - The Fundamental Theorem, Part 5

The Fundamental Theorem of Calculus. How an understanding of an incremental change in area helps lead to the fundamental theorem

From playlist Calculus - The Fundamental Theorem of Calculus

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Calculus - The Fundamental Theorem, Part 2

The Fundamental Theorem of Calculus. A discussion of the antiderivative function and how it relates to the area under a graph.

From playlist Calculus - The Fundamental Theorem of Calculus

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algebraic geometry 3 Bezout, Pappus, Pascal

This lecture is part of an online algebraic geometry course, based on chapter I of "Algebraic geometry" by Hartshorne. It gives more examples and applications of algebraic geometry, including Bezout's theorem, Pauppus's theorem, and Pascal's theorem.

From playlist Algebraic geometry I: Varieties

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Binomial Theorem- a quick introduction

TabletClass Math: https://tcmathacademy.com/ How to expand binomials using the binomial theorem. For more math help to include math lessons, practice problems and math tutorials check out my full math help program at https://tcmathacademy.com/ Math Notes: Pre-Algebra Notes:

From playlist Pre-Calculus / Trigonometry

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Beyond the Binomial Theorem: The Binomial Series

►Get my favorite, free calculator app for your phone or tablet: MAPLE CALCULATOR: https://www.maplesoft.com/products/maplecalculator/download.aspx?p=TC-9857 ►Check out MAPLE LEARN for your browser to do compute and graph math: https://www.maplesoft.com/products/learn/?p=TC-9857 ►Check out

From playlist Cool Math Series

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Discrete Math - 6.4.1 The Binomial Theorem

This is an introduction to the Binomial Theorem which allows us to use binomial coefficients to quickly determine the expansion of binomial expressions. Pascals Triangle is also covered. Textbook: Rosen, Discrete Mathematics and Its Applications, 7e Playlist: https://www.youtube.com/pla

From playlist Discrete Math I (Entire Course)

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Binomial Theorem Introduction to Raise Binomials to High Powers

I explain how Pascal's Triangle and the Binomial Theorem help you to quickly expand binomials raised to relatively high powers. My last example is using the Binomial Theorem to find a specific term within an expansion. New Binomial Theorem Lesson https://www.youtube.com/watch?v=VNmXwpa7

From playlist PreCalculus

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How to Use the Binomial Theorem (NancyPi)

MIT grad shows how to do a binomial expansion with the Binomial Theorem and/or Pascal's Triangle. To skip ahead: 1) for HOW TO EXPAND a BINOMIAL raised to a power, like (x + 3)^5, skip to time 0:57; 2) for how to find the BINOMIAL COEFFICIENTS with the FACTORIAL/COMBINATION formula, skip

From playlist Algebra 2

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AlgTop2: Homeomorphism and the group structure on a circle

This is the first video of the second lecture in this beginner's course on Algebraic Topology. We give the basic definition of homeomorphism between two topological spaces, and explain why the line and circle are not homeomorphic. Then we introduce the group structure on a circle, or in f

From playlist Algebraic Topology: a beginner's course - N J Wildberger

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Calculus: The Fundamental Theorem of Calculus

This is the second of two videos discussing Section 5.3 from Briggs/Cochran Calculus. In this section, I discuss both parts of the Fundamental Theorem of Calculus. I briefly discuss why the theorem is true, and work through several examples applying the theorem.

From playlist Calculus

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Pascal's Triangle and the Binomial Theorem | Don't Memorise

The concept of Pascal's Triangle helps us a lot in understanding the Binomial Theorem. Watch this video to know more... To watch more High School Math videos, click here - https://bit.ly/HighSchoolMath_DMYT Don’t Memorise brings learning to life through its captivating educational video

From playlist High School Math

Related pages

Hexagon | Bézout's theorem | Dandelin spheres | Degenerate conic | Desargues's theorem | Ellipse | Braikenridge–Maclaurin theorem | Affine plane | Cayley–Bacharach theorem | Synthetic geometry | Five points determine a conic | Line at infinity | Extended side | Parabola | August Ferdinand Möbius | Pole and polar | Thomas Kirkman | Euclidean plane | Similarity (geometry) | Pappus's hexagon theorem | Unicursal hexagram | Hyperbola | Edge (geometry) | Brianchon's theorem | Isogonal conjugate | Law of sines | Projective geometry | Projective plane | Conic section